5/50 Supplementary Question

[maureen1038]

Hi PAB

I should like to ask another question about the combinations in a 5/50 draw. Please forgive me if I use the wrong terminology.

I shall use the following line as an example of an ascending line in a 5/50 draw:

4 - 10 - 35 - 45 - 48

I call the result of subtracting a smaller number from its higher adjacent neighbour "the difference" .
So the line above contains the following 4 "differences"

6 - 25 - 10 - 3

and the lowest difference is 3.


At the moment , I am particularly interested in lowest differences.


I now know from your calculations in reply to my previous question that there are 748,006 combinations which contain consecutive numbers - i.e these combinations have a lowest difference of 1.

Is it possible to sub-divide the remaining 1,370,754 lines into groups according to their lowest differences? That is:

(i) the number of combinations with a lowest difference of 2

(ii) the number of combinations with a lowest difference of 3

and so on, up to

(xi) the number of combinations with a lowest difference of 12

Apologies for the length of this post.

Thanks

Maureen

 

[PAB]

Hi Maureen,

I should like to ask another question about the combinations in a 5/50 draw. Please forgive me if I use the wrong terminology.

I shall use the following line as an example of an ascending line in a 5/50 draw:

4 - 10 - 35 - 45 - 48

I call the result of subtracting a smaller number from its higher adjacent neighbour "the difference" .
So the line above contains the following 4 "differences"

6 - 25 - 10 - 3

and the lowest difference is 3.

At the moment, I am particularly interested in lowest differences.

We call this structure Delta Numbers if you are interested in doing a search on this Forum for an additional insight and information.

I now know from your calculations in reply to my previous question that there are 748,006 combinations which contain consecutive numbers - i.e these combinations have a lowest difference of 1.

Is it possible to sub-divide the remaining 1,370,754 lines into groups according to their lowest differences? That is:

(i) the number of combinations with a lowest difference of 2

(ii) the number of combinations with a lowest difference of 3

and so on, up to

(xi) the number of combinations with a lowest difference of 12

I will have a better look at your request a little bit later and hopefully post some statistical information for you.
I am glad you are enjoying the Forum, there is certainly a wealth of knowledge here to be found!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[PAB]

Hi Maureen,

Here are the statistics for the combined Lowest Delta's within EACH combination for a C(50, 5) Lotto from 1-12.

Lowest Delta 01 = 748,006 combinations.
Lowest Delta 02 = 520,086 combinations.
Lowest Delta 03 = 348,726 combinations.
Lowest Delta 04 = 223,686 combinations.
Lowest Delta 05 = 135,750 combinations.
Lowest Delta 06 = 76,726 combinations.
Lowest Delta 07 = 39,446 combinations.
Lowest Delta 08 = 17,766 combinations.
Lowest Delta 09 = 6,566 combinations.
Lowest Delta 10 = 1,750 combinations.
Lowest Delta 11 = 246 combinations.
Lowest Delta 12 = 6 combinations.
Total = 2,118,760 combinations.

I hope this helps!

Please let me know if this is OK!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.

 

[maureen1038]

Thank you PAB! This is wonderful! It is exactly what I wanted.

I have taken your advice, and read the posts concerning Delta Numbers. I had looked at these before (I have been lurking for a long time), and I noticed occasional differences in the way Delta Numbers are defined. A few people include the first number of a line as a Delta Number: but this would have given a lowest delta of 1 to all lines beginning with 1, and I did not want this.

One poster even suggested putting the combination into a circle, so that in my specimen line above, 4 and 48 would be adjacent numbers. This way of looking at things would be far too complicated for a simple soul such as I!

I shall stick with what seems to be the most commonly accepted definition, namely that a Pick 5 line contains 4 deltas, and a Pick 6 line contains 5 deltas.

Once again, PAB, thanks for all you advice and hard work. I see you have been very busy this weekend with requests for information . I'll let you have a few days rest before I bombard you with any more questions!

Best wishes, and thanks

Maureen

 

[PAB]

Hi Maureen,

Thank you PAB! This is wonderful! It is exactly what I wanted.

You are very welcome Maureen!

I have taken your advice, and read the posts concerning Delta Numbers. I had looked at these before (I have been lurking for a long time), and I noticed occasional differences in the way Delta Numbers are defined. A few people include the first number of a line as a Delta Number: but this would have given a Lowest Delta of 1 to all lines beginning with 1, and I did not want this.

Using the first number of a combination as the first Delta number is actually the correct way to calculate Delta numbers, but as you say, for statistical analysis such as you required, this would have given ambiguous results.
The Delta statistics that I keep include and exclude the first combination number, depending on what statistical results I am trying to achieve.

One poster even suggested putting the combination into a circle, so that in my specimen line above, 4 and 48 would be adjacent numbers. This way of looking at things would be far too complicated for a simple soul such as I!

I shall stick with what seems to be the most commonly accepted definition, namely that a Pick 5 line contains 4 deltas, and a Pick 6 line contains 5 deltas.

Yes, using the numbers in that way as an infinite loop is an interesting strategy, I remember reading that thread in the past. I might re-address that concept in the future and do some work on it when I get a spare five minutes!

Once again, PAB, thanks for all you advice and hard work. I see you have been very busy this weekend with requests for information. I'll let you have a few days rest before I bombard you with any more questions!

Just as a side note, if you have a spare minute and a half, the link below describes how to calculate Delta numbers as well as generating a combination from Delta numbers, which obviously uses a much smaller data set of numbers initially.

http://www.youtube.com/watch?v=pfVZSaMSZvU

Have FUN!

Regards,
PAB


-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-∏-
12:45, restate my assumptions.
(1) Mathematics is the language of nature.
(2) Everything around us can be represented and understood through numbers.
(3) If you graph the numbers of any system, patterns emerge. Therefore, there are patterns, everywhere in nature.